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ganeshie8
 one year ago
Just want to share this neat idea for why \(\times=+\)
ganeshie8
 one year ago
Just want to share this neat idea for why \(\times=+\)

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karatechopper
 one year ago
Best ResponseYou've already chosen the best response.0oh oh oh go I'm listening! :D

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.9let \(r_1\) and \(r_2\) be two positive numbers, then : \[\large (r_1)(r_2) = (r_1e^{i\pi})(r_2e^{i\pi})=r_1r_2e^{i2\pi}=r_1r_2\]

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.0that wouls also explain why ×+= i loved it

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.9didn't want to add anything as it looks so elegant+complete as an one liner xD But here some explanation : To multiply two complex numbers, we simply "multiply the two lengths" to get the resulting length and "add the two angles" to get the resulting angle. \[(r_1,\theta_1)*(r_2,\theta_2)=(r_1r_2,~\theta_1+\theta_2)\] Next notice that the angle for any negative number is \(\pi\) as they fall on the negative real axis. Consequently, multiplying two negative numbers adds up the angles\((\pi+\pi)\) taking the result to positive real axis.
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